If $x = - 1$ Is a Root Of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$

question 57

Multiple Choice

If $x = - 1$ is a root of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

• A) \(( x - 2 ) ( x + 1 ) ( x - 1 ) ; x = 2 , - 1,1\)
• B) \(( x + 2 ) ( x + 1 ) ( x - 1 ) ; x = - 2 , - 1,1\)
• C) \(( x + 2 ) ( x + 1 ) ^ { 2 } ; x = - 2 , - 1\)
• D) \(( x + 2 ) ^ { 2 } ( x + 1 ) ; x = - 2 , - 1\)
• E) \(( x + 2 ) ( x - 2 ) ( x - 1 ) ; x = - 2,2,1\)

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Definitions:

Frequency Detection

The ability of a system or organism to perceive and respond to specific frequencies of sound or electromagnetic waves.

Basilar Membrane

A key structure in the cochlea of the inner ear, it vibrates in response to sound, playing a critical role in the mechanical to neural transduction of sound.

Cochlea

A spiral-shaped cavity of the inner ear that plays a key role in converting sound waves into electrical signals for the brain to interpret as sound.

Ossicle

Small bones in the middle ear that transmit sound vibrations from the eardrum to the inner ear.